Be careful if you buy the property in cash, you will not be able to get a bank loan if you need to get some of your cash back for about a year. New rule so that home owners don't treat their house like an ATM.
Why would you use home equity instead of borrowing agaist the rental property where you get to write off interest as an expense against rental income? Even if you are in a position of taking a standard deduction you STILL get to write off the interest if the loan is against the rental property.
Refinancing the home at a lower rate to reduce your cost is an entirely different question.
I would definitely not do it. I like liquidity. You should only use your equity line for emergencies and not speculation, especially when it comes to housing. Real estate takes much patience and I don't think you'll make much money on rental property over next 10 years.
I think housing generally rents out for 6 to 9% of fair market value. By the time you add up interest expense, maintenance, property taxes, management fee, insurance etc. I don't think there is much left. Of course you can depreciate the property to shield income but it does lower your cost basis.